No Percolation in low temperature spin glass
Mathematical Physics
2016-10-11 v1 Disordered Systems and Neural Networks
math.MP
Probability
Abstract
We consider the Edwards-Anderson Ising Spin Glass model for non negative temperatures T: We define the natural notion of Boltzmann- Gibbs measure for the Edwards-Anderson spin glass at a given temperature, and of unsatisfied edges. We prove that for low enough temperatures, in almost every spin configuration the graph formed by the unsatisfied edges is made of finite connected components. In other words, the unsatisfied edges do not percolate.
Keywords
Cite
@article{arxiv.1610.02647,
title = {No Percolation in low temperature spin glass},
author = {Noam Berger and Ran J. Tessler},
journal= {arXiv preprint arXiv:1610.02647},
year = {2016}
}